Hostname: page-component-7479d7b7d-jwnkl Total loading time: 0 Render date: 2024-07-10T07:18:29.253Z Has data issue: false hasContentIssue false
  • English
  • Français

An uncertainty principle like Hardy's theorem for nilpotent Lie groups

Part of: Abstract harmonic analysis Lie groups

Published online by Cambridge University Press:  09 April 2009

Ajay Kumar  and
Chet Raj Bhatta
Ajay Kumar
Affiliation:
Department of Mathematics, Rajdhani College, (University of Delhi), Raja Garden, New Delhi - 110 015, India e-mail: ajaykr@bol.net.in
Chet Raj Bhatta
Affiliation:
Department of Mathematics, University of Delhi, Delhi - 110 007, India e-mail: crbhatta@yahoo.com
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We extend an uncertainty principle due to Cowling and Price to threadlike nilpotent Lie groups. This uncertainty principle is a generalization of a classical result due to Hardy. We are thus extending earlier work on Rn and Heisenberg groups.

Keywords

uncertainty principlenilpotent Lie groupFourier transformHilbert-Schmidt norm

MSC classification

Secondary: 22E25: Nilpotent and solvable Lie groups 43A30: Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 77 , Issue 1 , August 2004 , pp. 47 - 54
Copyright
Copyright © Australian Mathematical Society 2004

References

[1]Bagchi, S. C. and Ray, S. K., ‘Uncertainty principles like Hardy's theorem on some Lie groups’, J. Austral. Math. Soc. (Series A) 65 (1998), 289–302.CrossRefGoogle Scholar
[2]Corwin, L. and Greenleaf, F. P., Representations of nilpotent Lie groups and their applications, Part I. Basic theory and examples (Cambridge University Press, 1990).Google Scholar
[3]Cowling, M. G. and Price, J. F., ‘Generalizations of Heisenberg inequality’, in: Harmonic Analysis (Cartona 1982), Lecture Notes in Math. 992 (Springer, Berlin, 1983) pp. 443–449.CrossRefGoogle Scholar
[4]Dym, H. and Mckean, H. P., Fourier series and integrals (Academic Press, New York, 1972).Google Scholar
[5]Folland, G. B., A course in abstract harmonic analysis (CRC Press, Boca Raton, 1995).Google Scholar
[6]Hardy, G. H., ‘A theorem concerning Fourier transforms’, J. London Math. Soc. 8 (1993), 227–231.Google Scholar
[7]Kaniuth, E. and Kumar, A., ‘Hardy's theorem for simply connected nilpotent Lie groups’, Math. Proc. Cambridge Philos. Soc. 131 (2001), 487–494.CrossRefGoogle Scholar
[8]Morgan, G. W., ‘A note on Fourier transform’, J. London Math. Soc. 9 (1934), 187–192.CrossRefGoogle Scholar
[9]Nielson, O. A., Unitary representations and coadjoint orbits of low-dimensional nilpotent Lie groups, Queens Papers in Pure and Appl. Math. (Queen's Univ., Kingston, ON, 1983).Google Scholar